In the specific case of a watch or clock, it's perfectly acceptable to say "a watch that runs slow" or "a watch that runs fast". A clock that runs slow/fast and a clock that runs quickly/slowly are completely different meanings. In the first, the indicated time does not match the actual time. In the second, the perceived or relative time is passing slowly or quickly.
– ColleenVMar 22 '16 at 16:30